{
  "id": 2644,
  "curve_key": "1670918113:-13989710451025",
  "ainvs": [
    "1",
    "0",
    "0",
    "-34810794",
    "16188893604"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 63.709917241714024,
  "faltings_height": 3.374801115444702,
  "conductor": "1805874",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "31",
    "73"
  ],
  "discriminant": "2586479630436462323130624",
  "regulator": "7.98285207880755937069446362256433119612161",
  "points": [
    [
      "1423530",
      "-1699136262"
    ],
    [
      "316704",
      "-178357338"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1468 via the rational 2-torsion point x=-3745/4. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:15:02",
  "updated_at": "2026-09-26 20:15:02"
}